Question

Find and equation for the line with the given properties. Express the equation in general form. Slope -6/7; containing the point (10,-9) what is the equation for the line?

Answer 1

`6x+7y+3=0`

Explanation:

We are asked to find the equation of the line in general form, which has a of -6/7 and containing the point (10,-9).

We know that genera equation of a line is in form
`Ax+By+C=0`, where, A, B and C are real numbers.

First of all, we will write our equation in point-slope form as:

`y-y_1=m(x-x_1)`, where,

m = Slope of line,

`(x_1,y_1)` = Given point on line.

`y-(-9)=-(6)/(7)(x-10)`

`y+9=-(6)/(7)x+(60)/(7)`

`y*7+9*7=-(6)/(7)x*7+(60)/(7)*7`

`7y+63=-6x+60`

`6x+7y+63-60=-6x+6x+60-60`

`6x+7y+3=0`

Therefore, our required equation would be
`6x+7y+3=0`.